Fast and highly accurate computation of Chebyshev expansion coefficients of analytic functions · HackerPapers discussions

Fast and highly accurate computation of Chebyshev expansion coefficients of analytic functions — mentioned by jacobolus

Sat, 13 May 2017 05:55:42 GMT

(Disclaimer: I’m not a numerical analyst or hardware expert.) I’m not sure if you can use a dot product unit like the one in your link to make as much of a difference when handling recurrences like “Clenshaw’s algorithm” for evaluating Chebyshev polynomials (the method used in the OP, an analog of Horner’s algorithm), as you can get for taking a big dot product or computing an FFT or whatever. What I expect you really want is to keep your temporary variables in higher precision all the way through the recurrence. You can probably get some improvement vs. separate floating point addition and…

Paper and discussion history. A mention is not an endorsement.

Fast and highly accurate computation of Chebyshev expansion coefficients of analytic functions — mentioned by jacobolus

Sat, 03 Oct 2015 06:13:18 GMT

Yay for functions which are analytic in some neighborhood. Here’s the original paper from the 60s about the idea in this post: http://www.math.fsu.edu/~okhanmoh/media/Lyness,%20Moler,%20S... The latest work on this general topic is http://arxiv.org/pdf/1404.2463.pdf which manages to compute extremely accurate high-order derivatives (“...even the 100th derivative of an analytic function can be computed with near machine precision accuracy using standard floating point arithmetic”!!!), see also http://www.chebfun.org/examples/cheb/Turbo.html * * * Anyhow, for folks trying to take derivatives of…

Paper and discussion history. A mention is not an endorsement.